%% $Id: pst-fp.tex 276 2021-09-27 11:28:22Z herbert $

%% $Id: pst-fp.tex 276 2021-09-27 11:28:22Z herbert $
%%
%%
%% This is file `pst-fp.tex',
%%
%% IMPORTANT NOTICE:
%%
%% Package `pst-fp.tex'
%%
%% Herbert Voss <[email protected]>
%% "stolen" from the fp package by Michael Mehlich
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% DESCRIPTION:
%% `pst-fp' is a PSTricks related package for a division,
%% multiplication and addition
%%
%
\def\fileversion{0.06}
\def\filedate{2020/11/20}
\message{`pst-fp' v\fileversion, \filedate\space (hv)}

\csname PSTFPloaded\endcsname
\let\PSTFPloaded\endinput
% Requires some packages
\ifx\PSTricksLoaded\endinput\else\input pstricks \fi
%
\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax

%fixed point arithmetic with values between (including)
% -999999999999999999.999999999999999999
% and +999999999999999999.999999999999999999

\def\pstFPadd#1#2#3{\pstFP@callc\pstFP@add#1{#2}{#3}+\relax} % #1 := #2+#3
\def\pstFPsub#1#2#3{\pstFP@callc\pstFP@add#1{#2}{-#3}-\relax}% #1 := #2-#3
\def\pstFPmul#1#2#3{\pstFP@callc\pstFP@mul#1{#2}{#3}} % #1 := #2*#3
\def\pstFPdiv#1#2#3{\pstFP@callc\pstFP@div#1{#2}{#3}} % #1 := #2/#3

\def\pst@int#1{\expandafter\pst@@int#1..\@nil}
\def\pst@@int#1.#2.\@nil{#1}
\def\pst@Int#1{%
\@tempdima=#1\relax%
\expandafter\pst@@Int\the\@tempdima\@nil}
\def\pst@@Int#1.#2\@nil{#1}

%
\def\pstFPMul#1#2#3{\pstFP@callc\pstFP@mul#1{#2}{#3}% % #1 := int(#2*#3)
\edef#1{\pst@int{#1}}}%
\def\pstFPDiv#1#2#3{\pstFP@callc\pstFP@div#1{#2}{#3}% % #1 := int(#2/#3)
\edef#1{\pst@int{#1}}}%
\def\pstFPstripZeros#1#2{\pst@dimm=#1pt\relax \edef#2{\strip@pt\pst@dimm}}
%
\countdef\pstFP@actcounter=10 % register 0 for counter
\ifnum\pstFP@actcounter<60\relax \pstFP@actcounter=60\fi

\newcount\pstFP@xs %sign of 1st value
\newcount\pstFP@xia%integer part of 1st value
\newcount\pstFP@xib%integer part of 1st value
\newcount\pstFP@xfa%fractional part of 1st value
\newcount\pstFP@xfb%fractional part of 1st value

\countdef\pstFP@ys=5 %sign of 2nd value
\countdef\pstFP@yia=6%integer part of 2nd value
\countdef\pstFP@yib=7%integer part of 2nd value
\countdef\pstFP@yfa=8%fractional part of 2nd value
\countdef\pstFP@yfb=9%fractional part of 2nd value

\countdef\pstFP@xk=10 %registers for splitting 1st value
\countdef\pstFP@xl=11
\countdef\pstFP@xm=12
\countdef\pstFP@xn=13
\countdef\pstFP@xo=14
\countdef\pstFP@xp=15
\countdef\pstFP@xq=16
\countdef\pstFP@xr=17
\countdef\pstFP@xz=18
\countdef\pstFP@xt=19
\countdef\pstFP@xu=20
\countdef\pstFP@xv=21

\countdef\pstFP@yk=22 %registers for splitting 2nd value
\countdef\pstFP@yl=23
\countdef\pstFP@ym=24
\countdef\pstFP@yn=25
\countdef\pstFP@yo=26
\countdef\pstFP@yp=27
\countdef\pstFP@yq=28
\countdef\pstFP@yr=29
\countdef\pstFP@yz=30
\countdef\pstFP@yt=31
\countdef\pstFP@yu=32
\countdef\pstFP@yv=33

\newcount\pstFP@rega %auxiliary registers
\newcount\pstFP@regb
\countdef\pstFP@regc=36
\countdef\pstFP@regd=37
\countdef\pstFP@rege=38

\countdef\pstFP@rs=39 %result registers
\countdef\pstFP@ria=40
\countdef\pstFP@rib=41
\countdef\pstFP@rfa=42
\countdef\pstFP@rfb=43

\newcount\pstFP@regs %local auxiliary registers
\countdef\pstFP@count=45
\countdef\pstFP@res=46
\countdef\pstFP@shift=47
\newcount\pstFP@times
\countdef\pstFP@prod=49

%auxiliary macros which may be used in all of the following macros
\newif\ifpstFP@test

\def\pstFP@ignorenext#1{}
\def\pstFP@first#1#2\relax{#1}
\def\pstFP@swallow#1\relax{}
%
\def\ifpstFP@zero#1{%
\ifnum
\expandafter\ifnum\csname pstFP@#1ia\endcsname=0 0\else1\fi
\expandafter\ifnum\csname pstFP@#1ib\endcsname=0 0\else1\fi
\expandafter\ifnum\csname pstFP@#1fa\endcsname=0 0\else1\fi
\expandafter\ifnum\csname pstFP@#1fb\endcsname=0 0\else1\fi%
=0\relax
}
%
%read value
%
\def\pstFP@correctintcounter#1\relax{%
{\edef\pstFP@tmp{#1}%
\pstFP@count=0\relax%
\loop%
\edef\pstFP@tmpa{\expandafter\pstFP@first\pstFP@tmp\noexpand\relax}%
\expandafter\ifx\pstFP@tmpa0\relax%
\advance\pstFP@count1\relax%
\edef\pstFP@tmp{\expandafter\pstFP@ignorenext\pstFP@tmp}%
\repeat%
\ifnum\pstFP@count>18\relax \typeout{>>>> Overflow}\fi%
\expandafter\if!\pstFP@tmp!%
\advance\pstFP@count-18\relax%
\pstFP@count=-\pstFP@count%
\loop%
\ifnum\pstFP@count>0\relax%
\pstFP@regc=\pstFP@rega%
\divide\pstFP@rega10\relax\multiply\pstFP@rega10\relax%
\advance\pstFP@regc-\pstFP@rega\multiply\pstFP@regc100000000\relax%
\divide\pstFP@rega10\relax%
\divide\pstFP@regb10\relax\advance\pstFP@regb\pstFP@regc%
\advance\pstFP@count-1\relax%
\repeat%
\global\pstFP@rega=\pstFP@rega%
\global\pstFP@regb=\pstFP@regb%
\else%
\typeout{>>>>Number too big}%
\fi%
}%
}
\def\pstFP@@setintcounter#1#2#3#4#5#6#7#8#9{%
\pstFP@regb=#1#2#3#4#5#6#7#8#9\relax%
\pstFP@correctintcounter%
}
\def\pstFP@setintcounter#1#2#3#4#5#6#7#8#9{%
\pstFP@rega=#1#2#3#4#5#6#7#8#9\relax%
\pstFP@@setintcounter%
}

\def\pstFP@@setfractcounter#1#2#3#4#5#6#7#8#9{%
\pstFP@regb=#1#2#3#4#5#6#7#8#9\relax%
\pstFP@swallow%
}
\def\pstFP@setfractcounter#1#2#3#4#5#6#7#8#9{%
\pstFP@rega=#1#2#3#4#5#6#7#8#9\relax%
\pstFP@@setfractcounter%
}

\def\pstFP@getsign#1\relax{%
{\pstFP@regs=1\relax%
\edef\pstFP@tmp{#1}%
\loop%
\edef\pstFP@tmpa{\expandafter\pstFP@first\pstFP@tmp\noexpand\relax}%
\expandafter\ifx\pstFP@tmpa-\relax%
\multiply\pstFP@regs-1\relax%
\fi%
\ifnum\expandafter\ifx\pstFP@tmpa-1\else0\fi\expandafter\ifx\pstFP@tmpa+1\else0\fi>0%
\edef\pstFP@tmp{\expandafter\pstFP@ignorenext\pstFP@tmp}%
\repeat%
\global\let\pstFP@tmp\pstFP@tmp%
\global\pstFP@regs=\pstFP@regs%
}%
}

\def\pstFP@removeleadingzeros#1\relax{%
{\edef\pstFP@tmp{#1}%
\loop%
\edef\pstFP@tmpa{\expandafter\pstFP@first\pstFP@tmp\noexpand\relax}%
\expandafter\ifx\pstFP@tmpa0\relax%
\edef\pstFP@tmp{\expandafter\pstFP@ignorenext\pstFP@tmp}%
\repeat%
\global\let\pstFP@tmp\pstFP@tmp%
}%
}

\newif\ifpstFP@nonstop
\def\pstFP@strip#1{%
{\edef\pstFP@tmp{#1}%
\edef\pstFP@tmpb{}%
\ifx\pstFP@tmp\@empty\else%
\pstFP@nonstoptrue%
\loop%
\edef\pstFP@tmpa{\expandafter\pstFP@first\pstFP@tmp\noexpand\relax}%
\expandafter\ifx\pstFP@tmpa-\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa+\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa0\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa1\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa2\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa3\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa4\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa5\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa6\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa7\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa8\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\expandafter\ifx\pstFP@tmpa9\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
\ifx\pstFP@tmpa\@empty\pstFP@nonstopfalse\else%
\ifx\pstFP@tmpa\space\pstFP@nonstopfalse\else%
\typeout{>>> Illegal character \pstFP@tmpa\space found in float number}%
\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi%
\edef\pstFP@tmp{\expandafter\pstFP@ignorenext\pstFP@tmp}%
\ifx\pstFP@tmp\@empty\pstFP@nonstopfalse\fi%
\ifpstFP@nonstop%
\repeat%
\fi%
\global\let\pstFP@tmp\pstFP@tmpb%
}%
}

\def\pstFP@readvalue#1#2#3{%
% #1 macro family to catch the value
% #2.#3 value
%
% regular expression [+|-]*[d]_0^18.[d]*
%
\pstFP@strip{#2}%
%sign
\expandafter\pstFP@getsign\pstFP@tmp\relax%
\csname pstFP@#1s\endcsname=\pstFP@regs%
%
%integer part
\pstFP@removeleadingzeros\pstFP@tmp\relax%
\expandafter\pstFP@setintcounter\pstFP@tmp000000000000000000\relax%
\csname pstFP@#1ia\endcsname=\pstFP@rega%
\csname pstFP@#1ib\endcsname=\pstFP@regb%
%
%fractional part
\pstFP@strip{#3}%
\expandafter\pstFP@setfractcounter\pstFP@tmp000000000000000000\relax%
\csname pstFP@#1fa\endcsname=\pstFP@rega%
\csname pstFP@#1fb\endcsname=\pstFP@regb%
%
%correct sign
\ifnum\pstFP@rega=0\relax%
\ifnum\pstFP@regb=0\relax%
\expandafter\ifnum\csname pstFP@#1ib\endcsname=0\relax%
\expandafter\ifnum\csname pstFP@#1ia\endcsname=0\relax%
\csname pstFP@#1s\endcsname=1\relax%
\fi%
\fi%
\fi%
\fi%
}
%
%store value in macro
%
\def\pstFP@store#1#2{%
% #1 macro
% #2 macro family (value) to store
%
\ifpstFP@zero{#2}%
\csname pstFP@#2s\endcsname=1\relax%
\fi%
\expandafter\ifnum\csname pstFP@#2s\endcsname<0\relax%
\edef#1{-}%
\else%
\edef#1{}%
\fi%
\expandafter\ifnum\csname pstFP@#2ia\endcsname=0\relax%
\expandafter\ifnum\csname pstFP@#2ib\endcsname=0\relax%
\edef#1{#10}%
\else%
\edef#1{#1\expandafter\the\csname pstFP@#2ib\endcsname}%
\fi%
\else%
\expandafter\advance\csname pstFP@#2ib\endcsname1000000000\relax%
\edef#1{#1\expandafter\the\csname pstFP@#2ia\endcsname\expandafter\pstFP@ignorenext\the\csname pstFP@#2ib\endcsname}%
\fi%
\expandafter\advance\csname pstFP@#2fa\endcsname1000000000\relax%
\expandafter\advance\csname pstFP@#2fb\endcsname1000000000\relax%
\edef#1{#1\noexpand.\expandafter\pstFP@ignorenext\the\csname pstFP@#2fa\endcsname\expandafter\pstFP@ignorenext\the\csname pstFP@#2fb\endcsname}%
}
%macros to expand some arguments
%
\def\pstFP@callc#1#2#3#4{%
% #1 macro to call
% #2 macro, which gets the result
% #3 1st value
% #4 2nd value
% expand the values and split them into the integer and the fractional parts
\edef\next{\noexpand#1\noexpand#2#3..\noexpand\relax#4..\noexpand\relax}%
\next%
}
%
\def\pstFP@divten#1{%
\expandafter\pstFP@regc\csname pstFP@#1ia\endcsname%
\expandafter\divide\csname pstFP@#1ia\endcsname10\relax%
\expandafter\pstFP@regb\csname pstFP@#1ia\endcsname%
\multiply\pstFP@regb10\relax%
\advance\pstFP@regc-\pstFP@regb%
\multiply\pstFP@regc100000000\relax%
%
\expandafter\pstFP@rega\csname pstFP@#1ib\endcsname%
\expandafter\divide\csname pstFP@#1ib\endcsname10\relax%
\expandafter\pstFP@regb\csname pstFP@#1ib\endcsname%
\multiply\pstFP@regb10\relax%
\advance\pstFP@rega-\pstFP@regb%
\multiply\pstFP@rega100000000\relax%
\expandafter\advance\csname pstFP@#1ib\endcsname\pstFP@regc%
%
\expandafter\pstFP@regc\csname pstFP@#1fa\endcsname%
\expandafter\divide\csname pstFP@#1fa\endcsname10\relax%
\expandafter\pstFP@regb\csname pstFP@#1fa\endcsname%
\multiply\pstFP@regb10\relax%
\advance\pstFP@regc-\pstFP@regb%
\multiply\pstFP@regc100000000\relax%
\expandafter\advance\csname pstFP@#1fa\endcsname\pstFP@rega%
%
\expandafter\divide\csname pstFP@#1fb\endcsname10\relax%
\expandafter\advance\csname pstFP@#1fb\endcsname\pstFP@regc%
}
%
\def\pstFP@multen#1{%
\expandafter\multiply\csname pstFP@#1ia\endcsname10\relax%
\expandafter\ifnum\csname pstFP@#1ib\endcsname<100000000\relax%
\else%
\expandafter\pstFP@regc\csname pstFP@#1ib\endcsname%
\divide\pstFP@regc100000000%
\expandafter\advance\csname pstFP@#1ia\endcsname\pstFP@regc%
\multiply\pstFP@regc100000000%
\expandafter\advance\csname pstFP@#1ib\endcsname-\pstFP@regc%
\fi%
\expandafter\multiply\csname pstFP@#1ib\endcsname10\relax%
\expandafter\ifnum\csname pstFP@#1fa\endcsname<100000000\relax%
\else%
\expandafter\pstFP@regc\csname pstFP@#1fa\endcsname%
\divide\pstFP@regc100000000%
\expandafter\advance\csname pstFP@#1ib\endcsname\pstFP@regc%
\multiply\pstFP@regc100000000%
\expandafter\advance\csname pstFP@#1fa\endcsname-\pstFP@regc%
\fi%
\expandafter\multiply\csname pstFP@#1fa\endcsname10\relax%
\expandafter\ifnum\csname pstFP@#1fb\endcsname<100000000\relax%
\else%
\expandafter\pstFP@regc\csname pstFP@#1fb\endcsname%
\divide\pstFP@regc100000000%
\expandafter\advance\csname pstFP@#1fa\endcsname\pstFP@regc%
\multiply\pstFP@regc100000000%
\expandafter\advance\csname pstFP@#1fb\endcsname-\pstFP@regc%
\fi%
\expandafter\multiply\csname pstFP@#1fb\endcsname10\relax%
}
%
\def\pstFP@counttimes{%
{\global\pstFP@times=0\relax%
\loop%
\ifnum%
\ifnum\pstFP@xia>\pstFP@yia1%
\else\ifnum\pstFP@xia<\pstFP@yia0%
\else%
\ifnum\pstFP@xib>\pstFP@yib1%
\else\ifnum\pstFP@xib<\pstFP@yib0%
\else%
\ifnum\pstFP@xfa>\pstFP@yfa1%
\else\ifnum\pstFP@xfa<\pstFP@yfa0%
\else%
\ifnum\pstFP@xfb>\pstFP@yfb1%
\else\ifnum\pstFP@xfb<\pstFP@yfb0%
\else%
1%
\fi\fi%
\fi\fi%
\fi\fi%
\fi\fi%
=1\relax%
\global\advance\pstFP@times1\relax%
\global\advance\pstFP@xfb-\pstFP@yfb%
\ifnum\pstFP@xfb<0\relax%
\global\advance\pstFP@xfb1000000000\relax%
\global\advance\pstFP@xfa-1\relax%
\fi%
\global\advance\pstFP@xfa-\pstFP@yfa%
\ifnum\pstFP@xfa<0\relax%
\global\advance\pstFP@xfa1000000000\relax%
\global\advance\pstFP@xib-1\relax%
\fi%
\global\advance\pstFP@xib-\pstFP@yib%
\ifnum\pstFP@xib<0\relax%
\global\advance\pstFP@xib1000000000\relax%
\global\advance\pstFP@xia-1\relax%
\fi%
\global\advance\pstFP@xia-\pstFP@yia%
\repeat%
}%
}
%
\def\pstFP@add#1#2.#3.#4\relax#5.#6.#7\relax#8\relax{%
% #1 macro, which gets the result
% #2 integer part of 1st value
% #3 fractional part of 1st value
% #4 dummy to swallow everthing after the 2nd '.'
% #5 integer part of 2nd value
% #6 fractional part of 2nd value
% #7 dummy to swallow everthing after the 2nd '.'
%
{\pstFP@readvalue{x}{#2}{#3}%
\pstFP@readvalue{y}{#5}{#6}%
%
\ifnum\pstFP@xs=\pstFP@ys%
\advance\pstFP@xfb\pstFP@yfb%
\advance\pstFP@xfa\pstFP@yfa%
\ifnum\pstFP@xfb<1000000000\relax\else%
\advance\pstFP@xfb-1000000000\relax%
\advance\pstFP@xfa1\relax%
\fi%
\advance\pstFP@xib\pstFP@yib%
\ifnum\pstFP@xfa<1000000000\relax\else%
\advance\pstFP@xfa-1000000000\relax%
\advance\pstFP@xib1\relax%
\fi%
\advance\pstFP@xia\pstFP@yia%
\ifnum\pstFP@xib<1000000000\relax\else%
\advance\pstFP@xib-1000000000\relax%
\advance\pstFP@xia1\relax%
\fi%
\ifnum\pstFP@xia<1000000000\relax\else%
\pstFP@errmessage{Overflow}%
\fi%
\pstFP@store\pstFP@tmp{x}%
\else%
\advance\pstFP@xfb-\pstFP@yfb%
\ifnum\pstFP@xfb<0\relax%
\advance\pstFP@yfa1\relax%
\advance\pstFP@xfb1000000000\relax%
\fi%
\advance\pstFP@xfa-\pstFP@yfa%
\ifnum\pstFP@xfa<0\relax%
\advance\pstFP@yib1\relax%
\advance\pstFP@xfa1000000000\relax%
\fi%
\advance\pstFP@xib-\pstFP@yib%
\ifnum\pstFP@xib<0\relax%
\advance\pstFP@yia1\relax%
\advance\pstFP@xib1000000000\relax%
\fi%
\advance\pstFP@xia-\pstFP@yia%
\ifnum\pstFP@xia<0\relax%
\pstFP@xs=-\pstFP@xs%
\ifnum\pstFP@xfb=0\relax\else%
\advance\pstFP@xfb-1000000000\relax\pstFP@xfb=-\pstFP@xfb%
\advance\pstFP@xfa1\relax%
\fi%
\ifnum\pstFP@xfa=0\relax\else%
\advance\pstFP@xfa-1000000000\relax\pstFP@xfa=-\pstFP@xfa%
\advance\pstFP@xib1\relax%
\fi%
\ifnum\pstFP@xib=0\relax\else%
\advance\pstFP@xib-1000000000\relax\pstFP@xib=-\pstFP@xib%
\advance\pstFP@xia1\relax%
\fi%
\relax\pstFP@xia=-\pstFP@xia%
\fi%
\pstFP@store\pstFP@tmp{x}%
\fi%
\global\let\pstFP@tmp\pstFP@tmp%
}%
% \pstFPstripZeros\pstFP@tmp{#1}%
\let#1\pstFP@tmp
}

\def\pstFP@div#1#2.#3.#4\relax#5.#6.#7\relax{%
% #1 macro, which gets the result
% #2 integer part of 1st value
% #3 fractional part of 1st value
% #4 dummy to swallow everthing after the 2nd '.'
% #5 integer part of 2nd value
% #6 fractional part of 2nd value
% #7 dummy to swallow everthing after the 2nd '.'
%
% algorithmic idea (for x>0, y>0)
% - %determine \pstFP@shift such that y*10^\pstFP@shift <100000000<=y*10^(\pstFP@shift+1)
% - %determine \pstFP@shift' such that x*10^\pstFP@shift'<100000000<=x*10^(\pstFP@shift+1)
% - x=x*\pstFP@shift'
% - y=y*\pstFP@shift
% - \pstFP@shift=\pstFP@shift-\pstFP@shift'
% - res=0
% - while y>0 %fixed-point representation!
% - \pstFP@times=0
% - while x>y
% - \pstFP@times=\pstFP@times+1
% - x=x-y
% - end
% - y=y/10
% - res=10*res+\pstFP@times/1000000000
% - end
% - %shift the result according to \pstFP@shift
%
{\pstFP@readvalue{x}{#2}{#3}%
\pstFP@readvalue{y}{#5}{#6}%
%
%sign
\multiply\pstFP@xs\pstFP@ys%
\pstFP@rs=\pstFP@xs%
%
%compute division
\ifpstFP@zero{y}%
\typeout{>>>>Division by zero}%
\else%
\ifpstFP@zero{x}\def\next##1{\edef\pstFP@tmp{0}}\else\def\next##1{##1}\fi%
\next%
{\pstFP@shift=0\relax%
\loop%
\ifnum\pstFP@yia<100000000\relax%
\pstFP@multen{y}%
\advance\pstFP@shift1\relax%
\repeat%
\loop%
\ifnum\pstFP@xia<100000000\relax%
\pstFP@multen{x}%
\advance\pstFP@shift-1\relax%
\repeat%
\pstFP@ria=0\pstFP@rib=0\pstFP@rfa=0\pstFP@rfb=0\relax%
\loop%
\ifpstFP@zero{y}\else%
\pstFP@counttimes%divides x by \pstFP@times*y
\pstFP@divten{y}%
\pstFP@multen{r}%
\advance\pstFP@rfb\pstFP@times%
\ifnum\pstFP@rfb<1000000000\relax\else%
\advance\pstFP@rfa1\advance\pstFP@rfb-1000000000\relax%
\ifnum\pstFP@rfa<1000000000\relax\else%
\advance\pstFP@rib1\advance\pstFP@rfa-1000000000\relax%
\ifnum\pstFP@rib<1000000000\relax\else%
\advance\pstFP@ria1\advance\pstFP@rib-1000000000\relax%
\fi%
\fi%
\fi%
\repeat%
\loop%
\ifnum\pstFP@shift>17%
\advance\pstFP@shift-1\relax%
\ifnum\pstFP@ria<100000000\else\pstFP@ria=-1\fi%
\ifnum\pstFP@ria<0\pstFP@ria=-1\fi%
\pstFP@multen{r}%
\repeat%
\ifnum\pstFP@ria<1000000000\else\pstFP@ria=-1\fi%
\loop%
\ifnum\pstFP@shift<17%
\advance\pstFP@shift1\relax%
\pstFP@divten{r}%
\repeat%
\ifnum\pstFP@ria<0\relax%
\typeout{>>>>Overflow}%
\else%
\pstFP@store\pstFP@tmp{r}%
\fi%
}%
\fi%
%
\global\let\pstFP@tmp=\pstFP@tmp%
%
}%
% \pstFPstripZeros\pstFP@tmp{#1}%
\let#1\pstFP@tmp
}
%multiply two values

\def\pstFP@firstnine#1#2#3#4#5#6#7#8#9{%
\pstFP@res=#1#2#3#4#5#6#7#8#9\relax%
}
\def\pstFP@@ninesplit#1\relax#2\end#3{%
#1%
\edef#3{#2}%
}
\def\pstFP@ninesplit#1{%
\edef#1{\expandafter\pstFP@firstnine\pstFP@rd}%
\expandafter\pstFP@@ninesplit#1\end#1\relax%
}

\def\pstFP@split#1#2#3#4{%
% #1 highest three digits
% #2 medium three digits
% #3 least three digits
% #4 counter
\pstFP@regc=#4%
\divide\pstFP@regc1000000\relax%
#1=\pstFP@regc%
\multiply\pstFP@regc-1000000\relax\advance\pstFP@regc#4%
#3=\pstFP@regc%
\divide\pstFP@regc1000\relax%
#2=\pstFP@regc%
\multiply\pstFP@regc-1000\relax\advance\pstFP@regc#3%
#3=\pstFP@regc%
}

\def\pstFP@@mul#1#2#3{%
\pstFP@regc=\csname pstFP@x#1\endcsname%
\multiply\pstFP@regc\csname pstFP@y#2\endcsname%
\advance\pstFP@prod\pstFP@regc%
%
\ifx#3\relax%
\let\next=\relax%
\else%
\let\next=\pstFP@@mul%
\fi%
\next#3%
}

\def\pstFP@saveshift{%
% save rightmost three digits
\pstFP@regc=\pstFP@prod%
\divide\pstFP@prod1000\relax%
\multiply\pstFP@prod1000\relax%
\advance\pstFP@regc-\pstFP@prod%
\advance\pstFP@regc1000\relax%
\edef\pstFP@rd{\expandafter\pstFP@ignorenext\the\pstFP@regc\pstFP@rd}%
%
\divide\pstFP@prod1000\relax%
}

\def\pstFP@mul#1#2.#3.#4\relax#5.#6.#7\relax{%
% #1 macro, which gets the result
% #2 integer part of 1st value
% #3 fractional part of 1st value
% #4 dummy to swallow everthing after the 2nd '.'
% #5 integer part of 2nd value
% #6 fractional part of 2nd value
% #7 dummy to swallow everthing after the 2nd '.'
%
% split value in various parts
% x y = 123 456 789 123 456 789 . 123 456 789 123 456 789
% -> xk xl xm xn xo xp xq xr xs xt xu xv
% -> yk yl ym yn yo yp yq yr ys yt yu yv
% multiply these parts and save the result wrt the necessary shifts
%
{\pstFP@readvalue{x}{#2}{#3}%
\pstFP@readvalue{y}{#5}{#6}%
%
%sign
\multiply\pstFP@xs\pstFP@ys%
\pstFP@rs=\pstFP@xs%
%
% split parts
\pstFP@split\pstFP@xk\pstFP@xl\pstFP@xm\pstFP@xia\pstFP@split\pstFP@xn\pstFP@xo\pstFP@xp\pstFP@xib%
\pstFP@split\pstFP@xq\pstFP@xr\pstFP@xz\pstFP@xfa\pstFP@split\pstFP@xt\pstFP@xu\pstFP@xv\pstFP@xfb%
\pstFP@split\pstFP@yk\pstFP@yl\pstFP@ym\pstFP@yia\pstFP@split\pstFP@yn\pstFP@yo\pstFP@yp\pstFP@yib%
\pstFP@split\pstFP@yq\pstFP@yr\pstFP@yz\pstFP@yfa\pstFP@split\pstFP@yt\pstFP@yu\pstFP@yv\pstFP@yfb%
%
\pstFP@prod=0\relax%
\edef\pstFP@rd{}%
%
%compute result
\pstFP@@mul vv \relax\pstFP@saveshift%
\pstFP@@mul vu uv \relax\pstFP@saveshift%
\pstFP@@mul uu vt tv \relax\pstFP@saveshift%
\pstFP@@mul ut tu vz zv \relax\pstFP@saveshift%
\pstFP@@mul tt zu uz rv vr \relax\pstFP@saveshift%
\pstFP@@mul zt tz ur ru vq qv \relax\pstFP@saveshift%
\pstFP@@mul zz rt tr uq qu vp pv \relax\pstFP@saveshift%
\pstFP@@mul zr rz tq qt up pu vo ov \relax\pstFP@saveshift%
\pstFP@@mul rr qz zq tp pt uo ou vn nv \relax\pstFP@saveshift%
\pstFP@@mul rq qr zp pz to ot un nu vm mv \relax\pstFP@saveshift%
\pstFP@@mul qq rp pr zo oz tn nt um mu vl lv \relax\pstFP@saveshift%
\pstFP@@mul qp pq ro or zn nz tm mt ul lu kv vk \relax\pstFP@saveshift%
\pstFP@@mul pp oq qo rn nr zm mz tl lt ku uk \relax\pstFP@saveshift%
\pstFP@@mul op po nq qn rm mr zl lz tk kt \relax\pstFP@saveshift%
\pstFP@@mul oo pn np mq qm rl lr kz zk \relax\pstFP@saveshift%
\pstFP@@mul no on mp pm lq ql kr rk \relax\pstFP@saveshift%
\pstFP@@mul nn mo om pl lp qk kq \relax\pstFP@saveshift%
\pstFP@@mul mn nm lo ok pk kp \relax\pstFP@saveshift%
\pstFP@@mul mm ln nl ko ok \relax\pstFP@saveshift%
\pstFP@@mul lm ml kn nk \relax\pstFP@saveshift%
\pstFP@@mul ll km mk \relax\pstFP@saveshift%
\pstFP@@mul kl lk \relax\pstFP@saveshift%
\pstFP@@mul kk \relax\pstFP@saveshift\pstFP@saveshift%
\pstFP@ninesplit\pstFP@rd%
\ifnum\pstFP@res=0\relax%
\pstFP@ninesplit\pstFP@rd%
\ifnum\pstFP@res=0\relax%
\pstFP@ninesplit\pstFP@rd\pstFP@ria=\pstFP@res%
\pstFP@ninesplit\pstFP@rd\pstFP@rib=\pstFP@res%
\pstFP@ninesplit\pstFP@rd\pstFP@rfa=\pstFP@res%
\pstFP@ninesplit\pstFP@rd\pstFP@rfb=\pstFP@res%
\pstFP@store\pstFP@tmp{r}%
\else\typeout{pstFPmul: Overflow}\fi%
\else\typeout{pstFPmul: Overflow}\fi%
\global\let\pstFP@tmp\pstFP@tmp}%
% \pstFPstripZeros\pstFP@tmp{#1}%
\let#1\pstFP@tmp
}
%
\catcode`\@=\PstAtCode\relax
%
%% END: pst-fp.tex
\endinput